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Jim Dars science forum beginner
Joined: 03 Jul 2005
Posts: 41
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Posted: Tue Jun 20, 2006 7:49 pm Post subject:
Euler One
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Hi All,
I was just rereading William Dunham's "Euler - Master of Us All". Not as
good as his wonderful "Journey Through Genius", but still a VERY interesting
book.
He points out Euler's solution(s) to find the value of
Sum (1 to infinity on k) k^-i where i is an even integer (see Euler
Two)
and remarks that no one has yet found solutions for i being an odd integer
greater than one. (Except for the 1978 "find" that for i=3 the answer is
irrational.) Has any progress yet been made?
Best wishes, Jim |
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Frederick Williams science forum addict
Joined: 19 Nov 2005
Posts: 97
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Posted: Wed Jun 21, 2006 3:05 pm Post subject:
Re: Euler One
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Jim Dars wrote:
Quote: |
Hi All,
I was just rereading William Dunham's "Euler - Master of Us All". Not as
good as his wonderful "Journey Through Genius", but still a VERY interesting
book.
He points out Euler's solution(s) to find the value of
Sum (1 to infinity on k) k^-i where i is an even integer (see Euler
Two)
and remarks that no one has yet found solutions for i being an odd integer
greater than one. (Except for the 1978 "find" that for i=3 the answer is
irrational.) Has any progress yet been made?
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Yes, see http://mathworld.wolfram.com/RiemannZetaFunction.html.
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